An edge of a variable cube is increasing at the rate of 2 cm/s. How fast is the volume of the cube increasing when the edge is 12 cm long?

Let x be the length of a side and V be the volume of the cube. Then, v = x^{3}. dV/dt = 3x^{2} × dx/dt It is given that dx/dt = 2 cm/s dv/dt = 3x^{2}(2) = 6x^{2} Thus, when x = 12 cm dv/dt = 6 (12)^{2} = 864 cm^{3}/s

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